Pneumatic resistance and capacitance combinations (RC circuits) form the basis of many common pneumatic circuits. In calculating the dynamics of circuits, the characteristic equation (equation of state) is usually thought to be either an adiabatic or isothermal process. However, there is not a sufficient explanation for the phenomena concerned with these circuits, i. e., why the politropic index is bigger when the air is discharging from the capacitance than when it is charging. In order to explain these matters, it is necessary to deal with the energy balance in a capacitance on the basis of the First Law of Thermodynamics considering the conduction of heat.
In this research, the energy equation is solved assuming that the conduction of heat between the air and the wall of the capacitance is in proportion to the temperature difference. Calculations using this exact model of pneumatic RC circuits yield some satisfactory agreement with the experiment.

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The mathematical modelling of components which are used in oil hydraulic systems is one of the most important themes at present for predicting and improving the characteristics of the oil hydraulic systems. The dynamic behaviors of unsteady flows through chokes and other conduits in oil hydraulic components have a great influence upon the dynamic characteristics of the components. The length of these comparatively short conduits are considered to be within the inlet length.
In this study, the pressure drop frequency characteristics for flow rate in the inlet region of a circular tube is measured experimentally, and the theoretical values derived using an approximate solution for the velocity profiles for the oscillatory flow, which is shown in the author's previous work, are compared with the experimental results, not only to evaluate the unsteady pressure drop but also to investigate the dynamic behaviors of the flow near the tube wall which have not been clarified very well.

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